Conjecture and Question

[Neuge]

Consider this extreme situation. Let's say that you miraculously acquire someone's entire starting stack on every hand you play and no one else gains or loses chips (ignore blind and ante money for simplicity). You must knock out X% of people, minus 1 for yourself, to have equal equity as the X% payout for first place if you assume that your equity doubles with your chip stack. This essentially equates to 1st place payout equity if you start with X% of chips in play. Even in such an advantageous position you surely cannot be guaranteed to win the tournament 100% of the time.

This only assumes that you have $10,000 equity in a $10,000 tourney. Suppose you have Y x buyin equity (in your example Y=4), then if the conjecture is true you only have to knock out X/Y - 1 people before you are "guaranteed" to win.